Question

AB is a line segment and line l is its perpendicular bisector. Show that every point on line l is equidistant from A and B.

Answer 1

Consider $△PCA$ and $△PCB$

$AC=BC$ since $AC=BC$(given)

$\angle PCA=\angle PCB$ since line $l$ is perpendicular to $AB$

$PC=PC$(common)

$△PCA\cong △PCB$ by SAS congruence rule.

So, $PA=PB$ by CPCT

Hence proved.